Circuit for determining the effective series resistance and Q-factor of capacitors

Abstract

A meter circuit for measuring the effective series resistance (ESR) and Q-Factor of a capacitive device has an operational amplifier with an input to which a source of AC input voltage is applied. A feedback circuit is connected between output and input of the amplifier. A series network is connected between the feedback circuit and ground. This network has an inductor of known Q-Factor in series with a capacitive device whose Q-factor is to be determined. Voltmeters measure the applied input voltage and output voltage of the amplifier. Where the series resistances of the inductor and capacitive device at resonance frequency have a low total magnitude, the meter circuit can be modified by inserting a wideband transformer, having very low output impedance, in the feedback circuit in series with an adjustable gain operational amplifier.

What is claimed is: 
     
       1. A meter circuit for determining the Q-factor of a capacitive device, comprising, an operational amplifier having two input terminals and an output terminal having a measureable output voltage;   means for applying a measurable input voltage adjustable in frequency and magnitude to one of said input terminals of said amplifier;   a feedback circuit connected between the other one of said input terminals and said output terminal of said amplifier;   a resistor having a resistance of known magnitude in said feedback circuit; and   a network having one end connected in said feedback circuit between the junction of said resistor and said other one of said input terminals the other end grounded, said network comprising an inductor of known Q-factor and resistance and means connecting in series with said inductor a device of known capacitance whose Q-factor is to be determined, whereby when said circuit is caused to resonate, the Q-factor of said device is obtained by dividing the capacitance reactance of said device by the effective series resistance of said device obtained from said resistance, the series resonant resistance of said inductor, and the ratio of said output voltage to said input voltage of said amplifier.   
     
     
       2. A meter circuit as defined in claim 1, wherein said network has a resonance at a particular frequency of said input voltage, and wherein said Q-factor to be determined is expressed as: ##EQU10## wherein X cx  is a capacitive reactance of said device at said resonance frequency and equal to the inverse multiplication of the resonant frequency, said capacitance of said device, and 2π, and wherein ESR is an effective series resistance of said device at said resonance frequency of said network. 
     
     
       3. A meter circuit as defined in claim 2, further comprising means for measuring input and voltage across said output terminals of said amplifier, whereby said effective series resistance of said device is expressed as: ##EQU11## wherein R f  is said known resistance of said resistor in said feedback circuit, R L  is the series magnitude of said inductor at said resonance frequency of said network, and A is the gain of said amplifier expressed as a ratio of the voltage between said input and output terminals thereof. 
     
     
       4. A meter circuit as defined in claim 3, wherein said voltage measuring means are voltmeters respectively connected across said output and said input terminals of said amplifier. 
     
     
       5. A meter circuit as defined in claim 3 further comprising a wideband voltage stepdown transformer having a very low output impedance connected in said feedback circuit in series with said resistor therein; and another operational amplifier connected in said feedback circuit to compensate for the voltage reduction produced by said stepdown transformer, whereby said Q-factor of said device is accurately determined even though it has a high numerical value, and even though said series resistance of said inductor at said resonance frequency plus said effective series resistance of said device have a very low magnitude. 
     
     
       6. A meter circuit as defined in claim 5, wherein said other amplifier has other input and output terminals, and further comprising another feedback circuit connected between said other input and said output terminals and having an adjustable resistor therein for calibrating said other amplifier. 
     
     
       7. A meter circuit as defined in claim 6, further comprising a further operational amplifier connected in said first named feedback circuit between said transformer and said first named amplifier to serve as a buffer therebetween. 
     
     
       8. A meter circuit as defined in claim 7, further comprising other voltage measuring means for measuring said input voltage across said input terminals of said first named amplifier, and wherein said gain of said first amplifier is expressed as: ##EQU12## wherein V 2  is the magnitude of said output voltage measured by said first mentioned voltage measuring means, and V 1  is the magnitude of said input voltage measured by said other voltage measuring means. 
     
     
       9. A meter circuit as defined in claim 8, wherein said first mentioned and said other voltage measuring means are voltmeters respectively connected across said output terminals and said input terminals respectively of said first named amplifier.